Use adhesive and nails/screws when adding a layer over plaster. 3" screws are a bit of a stretch (unless you have 2" of plaster), will be expensive, and will be a pain to use. Consider new construction. Standard is 1-1/4" screws or 1-3/8" nails. Roughly 3/4" penetration into the framing lumber. Most plaster and lath is 1" thick (nominally). If you're using 1/4" rock, 2" fasteners are fine.....

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I'm assuming this is a first floor where you can't get in the attic and get an idea where to start. The joists SHOULD be running the shorter direction of the room size. I take a nail (8d, 16d, whatever you have on hand) and come off of the wall (parallel to the direction the joists are BELIEVED to be running) a foot or so and start "searching". Drive the nail in. If you don't hit anything, move over about an inch or so (either direction) and try again. Keep on until you hit something solid (wood). Measure over 16" and see if you hit something solid again. If not try 24". Basically, you're going "fishing" and hopefully the joists are on some kind of pattern. You really need to find each individual joist! Sometimes in older homes, they may not necessarily be on any certain centers. Be sure when you hit wood to find both sides of the joist (keep driving your nail on both sides until you hit "air". Make mark in the center of the joist. Go to the opposite end of the room and use your measurements to find the first joist on that side. Repeat the procedure to find the centers on that side too (things could be out of square). Chalk a line from one side to other on the center of the joists and you're good to go. If it was a sheetrock ceiling you're going over, once you find a joist you can use a "keyhole" saw to jab into the board, saw until you hit wood, then move over 3/4" to figure out the center of the joist....

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